Multiple Choice Practice Locus Geometry Level Geometry Index | Regents Exam Prep Center

 Also available in Hardcopy (.pdf): Locus

Directions:  Choose the best answer.  Answer ALL questions (or only a few at a time), then use the BUTTON at the BOTTOM of the page to check your answers.  If you are told that an answer is incorrect, go back and redo that question and CHECK ANSWERS again.   You may CHECK ANSWERS at any time.
You may use your graphing calculator when working on these problems.

1.  Point A and point B are 26 miles apart. How many points are 20 miles from point A and 22 miles from point B?
[1]  1                [2]  2                 [3]  3                [4]  0

2.  Perry, the squirrel, buried his favorite nuts 4 feet from the fence and equidistant from trees A and B. The fence, between the trees, is 6 feet long. What is the distance from his buried nuts to either tree A or B?
[1]  3 feet                [2]  4 feet
[3]  5 feet                [4]  6 feet

3.  How many point are equidistant from two parallel lines and also equidistant from two points on one of the lines?

[1]  1           [2]  2                  [3]  3               [4]  4

4.  In the coordinate plane, what is the total number of points 8 units from the origin and equidistant from both the x-axis and the y-axis?
[1]  1             [2]   2               [3]  3                [4]
4

5.  The locus of points equidistant from the points (-5,8) and (7,8) is the line whose equation is
[1]  y = 1        [2]  x = 1         [3]  y = 8           [4]  x = 8

 6.  What is the locus of points (in the plane) equidistant from the two sides of an angle?      [1]  the intersection of the perpendicular bisectors of the sides of the angle.      [2]  a circle with its center at the vertex of the angle.      [3]  the intersection of the lines which are parallel to the sides of the angle.      [4]  the angle bisector.

7.  What is the equation of the locus of points 5 units from the origin?

[1]  x = 5                [2]  y = 5               [3]  x² + y² = 5          [4]  x² + y² = 25

8.  What is the equation of the locus of points 10 units away from the y-axis?
[1]  y = 10
[2]  y = 10 or y = -10
[3]  x = 10
[4]  x = 10 or x = -10

9.  Two buoys are located at coordinates (-10,-3) and
(-2,-3). A scuba diver swims so that he is always equidistant from both buoys. What equation represents the line along which the diver swims?
[1]  y = -8             [2]  y = -6
[3]  x = -6             [4]  x = -8

10. What is the equation(s) of the locus of points equidistant from the lines x = -15 and x = 3?

[1]  x = -6        [2]  x = 9 and x = -21     [3]  x = -9         [4]  x = -9 and x = 0

11.  Ben skis on a path equidistant from point (9,14) and point (9, -10). What is the equation of the path skied by Ben?
[1]  y = 4x + 1
[2]  y = 2
[3]  x = 2
[4]  y = 2x + 9

12.  Two parallel lines are 10 units apart. Point A is located on one of the parallel lines. How many points are equidistant from the two parallel lines and are also 5 units from point A?

[1]  1        [2]  2          [3]  3         [4]  0

13. Two points C and D are located 12 feet apart. How many points are 6 feet from point C and 4 feet from point D?
[1]  1         [2]  2          [3]  0          [4] 4

14.  Fido, the dog, is temporarily tied to a ground stake while his nearby owner works on a sketch of a tree. If Fido's leash is 15 feet in length, what is the length of the locus path Fido can travel at the end of his leash?
[1]
[2]       [3]      [4]

15.  The locus of points at a fixed distance, d, from a line a, is
[1]  one line parallel to line a at a distance d away.
[2]  a circle with a radius of d.
[3]  a pair of parallel lines d distance from a and on either side of a.
[4]  a line perpendicular to line a.

16. Jason jogs on a path equidistant from the parallel sides of two buildings. His jog path is represented by
y = 4 and the side of building 1 is represented by
y = 1. Which equation represents the side of building 2?

[1] y = 5

[2] y = 7
[3] y = 8
[4] x = 3

17.

Which of the following points lies on the locus of points equidistant from points (4,5) and (6,5)?

[1]  (5,5)      [2]  (5,7)      [3]  (5,-12)      [4]  All of these points.

 18.  The locus of points equidistant from the lines x = -4.5 and x = 4.5 is      [1]  y = 0              [2]  x-axis              [3]  x = 1               [4]  y-axis

19.  How many points in the plane are equidistant form the points A(8,6), B(2,6) and C(4,4)?
[1]  1     [2]  2     [3]  3     [4]  4

20.  Indiana Jones (Indy) finds a clue which states, "Start at point B where the cliffs converge and walk through the canyon staying an equal distance from each cliff." If m<ABC = 86º, what is the measure of <DBC?

[1] 45º
[2] 62º

[3] 43º

[4] 38º